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A166634 Totally multiplicative sequence with a(p) = 4*(p-1) for prime p. 3
1, 4, 8, 16, 16, 32, 24, 64, 64, 64, 40, 128, 48, 96, 128, 256, 64, 256, 72, 256, 192, 160, 88, 512, 256, 192, 512, 384, 112, 512, 120, 1024, 320, 256, 384, 1024, 144, 288, 384, 1024, 160, 768, 168, 640, 1024, 352, 184, 2048, 576, 1024 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = (4*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)-1)^e(k). a(n) = A165825(n) * A003958(n) = 4^bigomega(n) * A003958(n) = 4^A001222(n) * A003958(n).

MATHEMATICA

DirichletInverse[f_][1] = 1/f[1]; DirichletInverse[f_][n_] :=

DirichletInverse[f][n] = -1/f[1]*Sum[f[n/d]*DirichletInverse[f][d], {d, Most[Divisors[n]]}]; muphi[n_] := MoebiusMu[n]*EulerPhi[n]; a[m_] := DirichletInverse[muphi][m]; Table[a[m]*4^(PrimeOmega[m]), {m, 1, 100}] (* G. C. Greubel, May 20 2016 *)

PROG

(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 4*(f[k, 1]-1)); factorback(f); } \\ Michel Marcus, May 20 2016

CROSSREFS

Cf. A001222, A003958, A165825, A166633.

Sequence in context: A312762 A312763 A312764 * A189007 A242349 A309521

Adjacent sequences:  A166631 A166632 A166633 * A166635 A166636 A166637

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Oct 18 2009

STATUS

approved

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Last modified September 26 13:34 EDT 2021. Contains 347668 sequences. (Running on oeis4.)